Sources of current are employed for fabricating rounded can bodies welded along the longitudinal seam and which generate an intermittent or periodic, nearly rectangular current in the pressure-roller electrodes are known in the prior art, as exemplified by West German Offenlegungsschrift No. 16 13 730 (U.S. Pat. No. 3,553,567) and Swiss Pat. No. 483 292 (British Pat. No. 1,180,979). To obtain a weld of the highest quality, alternating current pulses are utilized which have a higher frequency than the standard line or power network frequency. By using an alternating current, the danger of arcing which occurs in d.c. welding and the resultant destruction of the seam to be welded can largly be avoided. However, the use of a higher-frequency alternating current requires a considerable expenditure in circuitry, e.g., for the control of the start and end of the welding operation and for the control of the welding power to be used. However, another important disadvantage of the prior art welding processes which use a higher-frequency welding current is to be seen in the heating of the resistance welding apparatus which is caused by eddy currents. In addition to the electrical losses resulting therefrom, a non-negligible expenditure and technical effort is needed to cool the resistance welding apparatus, with the result that its efficiency is still further reduced. Additionally, in most resistance welding apparatus, special antimagnetic materials must be employed for many components in order to keep the eddy-current induced heating within controllable bounds.